From the Map
This will open the quick view popup for that record. Then you can click on the edit button in the upper right corner of the record quick view.
From the data table
You can also select the record from the table on the split/hybrid view or table view, by clicking the record options button on the far left of the record's row. Then in the record options menu select either 'quick view', 'open', or 'edit'.
If you select either 'open' or 'quick view' the record will not open directly into edit mode and you must click the same edit button like you would when access a record from the map. The 'edit' option will open the record in the quick view with edit mode already enabled.
The difference between the 'quick view' and the 'open' views is that the open option opens the record in a full page view in another browser tab, while the quick view displays the record data in a popup window over top of the record editor.
Save the record
Once you have finished editing the record, make sure that you save the record fully by pressing the green check box in the upper right corner of the edit window/page.
You can tell that the record is fully save once the colored bar across the top of the record changes from blue to red and the 'editing' text to the right of the record title disappears.